1. Field of the Invention
The present invention relates to a method of measuring values of a physical property, such as capacitance C or dielectric constant ∈, by detecting the electrostatic force acting between a probe and a sample. The invention also relates to apparatus, such as a scanning probe microscope (SPM), using this method.
2. Description of the Related Art
An atomic force microscope (AFM) is one kind of scanning probe microscope (SPM) and can image specimen surfaces at atomic-scale resolution. AFM provides a basis for various SPM techniques. Normal AFM can image surface topography. A procedure for imaging the distribution of values of a physical property near a sample surface, such as electric capacitance C or dielectric constant ∈, is scanning capacitance microscopy (SCM). Two methods have been proposed to measure capacitance C by AFM. In one method, a capacitance sensor is mounted close to the probe. In the other method, electrostatic force is detected and measured.
The prior art of this method using a capacitance sensor is described. Measurement of the electric capacitance C between a probe and a sample in a microscopic region was started by Matey et al. [J. R. Matey and J. Blanc, J. Appl. Phys. 47, 1437 (1985)] using a capacitance sensor of an electrostatic video disk player developed by RCA for consumer applications [R. C. Palmer, E. J. Denlinger, and H. Kawamoto, RCA Rev. 43, 194 (1982)]. Matey et al. did not control the probe-sample separation. However, Williams et al. succeeded in measuring capacitance C in a microscopic region by a capacitance sensor while controlling the probe-sample separation using scanning tunneling microscopy (STM) [C. C. Williams, W. P. Hough, and S. A. Rishton, Appl. Phys. Lett. 55, 203(1989)]. Furthermore, Barret et al. performed measurement of electric capacitance C on a silicon oxide film that is an insulator, using AFM [R. C. Barrett and C. F. Quate, J. Appl. Phys. 70, 2725 (1991)]. In this way, products that are commercially available as SCM are based on an instrument where a capacitance sensor is mounted close to an AFM probe.
RCA""s capacitance sensor is fitted with an oscillator oscillating at a fixed frequency. An LC resonator circuit is formed by the probe-sample capacitance C and the inductance L in the sensor. The resonant frequency of this LC resonator circuit varies. The amplitude of the output signal taken through the resonator circuit is detected using an amplitude detector. On the other hand, Cho et al. has proposed a capacitance sensor which uses a frequency variable oscillator whose oscillation frequency is varied by the probe-sample capacitance C and the inductance L in an externally attached sensor. The frequency of the output signal is detected by the use of a frequency detector [Y. Cho, A. Kirihara, and T. Saeki, Rev. Sci. Instrum. 67, 2297 (1996)].
With any capacitance sensor, the modulation method is used in practical operation to avoid the effects of stray capacitance. An AC electric field (alternating voltage) is applied between the probe and the sample. Amplitude or frequency modulated thereby is detected using a lock-in amplifier. Therefore, the actually obtained image is not an image of the distribution of electric capacitances C, but an image of the distribution of differential capacitances (∂C/∂V). In this method, the probe-sample separation is controlled by AFM technique. Detection of electric capacitance needs a special capacitance sensor and so the structure of the instrument is complex.
The prior art of the method by detecting electrostatic force is described. The prior art of the method using detection electrostatic force is described. Martin et al. proposed a method of detecting electric capacitance C on a sample surface using only AFM without employing a capacitance sensor [Y. Martin, D. W. Abraham, and H. K. Wickramasinghe, Appl. Phys. Lett. 52, 1103 (1988)]. In this method, an AC electric field E of frequency f (angular frequency xcfx89=2xcfx80f) is applied between a probe and a sample. The electrostatic force of the second harmonic component is detected. The principle of measurement is as follows. It is assumed that the probe-sample system is made up of flat metal plates parallel to each other. Let C be the capacitance. Let the direction vertical to the parallel plates be the Z-direction. When a voltage V is applied, an electrostatic force F given by Eq. (1) acts.                     F        =                              -                          1              2                                ⁢                                    ∂              C                                      ∂              z                                ⁢                      V            2                                              (        1        )            
If the voltage V applied between the probe and the sample is divided into a DC component Vdc and an AC component Vac, the voltage V is given by
V=Vdc+Vac cos xcfx89txe2x80x83xe2x80x83(2)
When this voltage V is applied, the electrostatic force F is given by                     F        =                              -                          1              4                                ⁢                                    ∂              C                                      ∂              z                                ⁢                      (                                          2                ⁢                                  V                                      d                    ⁢                                          xe2x80x83                                        ⁢                    c                                    2                                            +                              4                ⁢                                  V                                      d                    ⁢                                          xe2x80x83                                        ⁢                    c                                                  ⁢                                  V                                      a                    ⁢                                          xe2x80x83                                        ⁢                    c                                                              +                              V                                  a                  ⁢                                      xe2x80x83                                    ⁢                  c                                2                            +                                                V                                      a                    ⁢                                          xe2x80x83                                        ⁢                    c                                    2                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                t                                      )                                              (        3        )            
If the relation Vdc=0 is introduced, we have                     F        =                              -                          1              4                                ⁢                                    ∂              C                                      ∂              z                                ⁢                      (                                          V                                  a                  ⁢                                      xe2x80x83                                    ⁢                  c                                2                            +                                                V                                      a                    ⁢                                          xe2x80x83                                        ⁢                    c                                    2                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                t                                      )                                              (        4        )            
Since the value of Vac is known, the (∂C/∂z) component can be detected by detecting the second harmonic (2xcfx89) component. That is, the values of the physical property, such as capacitance C or dielectric constant ∈, can be measured.
In this method, however, a modulation method is not used, unlike the method using a capacitance sensor. Therefore, the effects of stray capacitance cannot be neglected and the sensitivity is low.
The present invention is intended to solve the foregoing problems.
It is an object of the invention to provide a method of measuring values of a physical property, such as capacitance C or dielectric constant ∈, by detecting electrostatic force, for example, without using any special capacitance sensor.
It is another object of the invention to provide a scanning probe microscope for implementing this method.
A method of measuring values of a physical property in accordance with the present invention consists of applying an AC voltage oscillating at an angular frequency of xcfx89 between a probe and a sample to thereby induce a force oscillating at an angular frequency of nxc3x97xcfx89 (nxe2x89xa73) and detecting the induced force. Thus, the values of the physical property, such as capacitance C or dielectric constant ∈, are measured.
In the conventional method using detection of an electrostatic force, a modulation method is not used as mentioned previously. Therefore, electric capacitance C is imaged instead of differential capacitance (∂C/∂V). Therefore, there are the effects of stray capacitances. In the present invention, to solve this problem, an AC voltage V of angular frequency of xcfx89 is applied between the probe and the sample. In this case, it is assumed that the probe-sample system consists of flat metal plates parallel to each other and has an electric capacitance of C. Let the z-axis vertical to the parallel plates. The component ∂C/∂z is not constant, but is modulated by the applied voltage V and so we consider that the component ∂C/∂z is modulated by the angular frequency xcfx89 as given by                                           ∂                          C              ⁡                              (                                  V                  ,                  z                                )                                                          ∂            z                          =                                            ∂                              C                ⁡                                  (                                                            V                                              d                        ⁢                                                  xe2x80x83                                                ⁢                        c                                                              ,                    z                                    )                                                                    ∂              z                                +                                                                      ∂                  2                                ⁢                                  C                  ⁡                                      (                                                                  V                                                  d                          ⁢                                                      xe2x80x83                                                    ⁢                          c                                                                    ,                      z                                        )                                                                                                ∂                  V                                ⁢                                  ∂                  z                                                      ⁢                          V                              a                ⁢                                  xe2x80x83                                ⁢                c                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢            ω            ⁢                          xe2x80x83                        ⁢            t                                              (        5        )            
Therefore, the electrostatic force is given by                     F        =                              -                          1              4                                ⁢                      (                                                            ∂                                      C                    ⁡                                          (                                                                        V                                                      d                            ⁢                                                          xe2x80x83                                                        ⁢                            c                                                                          ,                        z                                            )                                                                                        ∂                  z                                            +                                                                                          ∂                      2                                        ⁢                                          C                      ⁡                                              (                                                                              V                                                          d                              ⁢                                                              xe2x80x83                                                            ⁢                              c                                                                                ,                          z                                                )                                                                                                                        ∂                      V                                        ⁢                                          ∂                      z                                                                      ⁢                                  V                                      a                    ⁢                                          xe2x80x83                                        ⁢                    c                                                  ⁢                cos                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                t                                      )                    ⁢                      (                                          V                                  a                  ⁢                                      xe2x80x83                                    ⁢                  c                                2                            +                                                V                                      a                    ⁢                                          xe2x80x83                                        ⁢                    c                                    2                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                t                                      )                                              (        6        )            
This can be varied to:                                                         F              =                            ⁢                              -                                                      1                    4                                    [                                                                                                              ∂                                                      C                            ⁡                                                          (                                                                                                V                                                                      d                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    c                                                                                                  ,                                z                                                            )                                                                                                                                ∂                          z                                                                    ⁢                                              V                                                  a                          ⁢                                                      xe2x80x83                                                    ⁢                          c                                                2                                                              +                                                                                                                        ∂                            2                                                    ⁢                                                      C                            ⁡                                                          (                                                                                                V                                                                      d                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    c                                                                                                  ,                                z                                                            )                                                                                                                                                            ∂                            V                                                    ⁢                                                      ∂                            z                                                                                              ⁢                                              V                                                  a                          ⁢                                                      xe2x80x83                                                    ⁢                          c                                                3                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                                        +                                                                                                                                        ⁢                                                                                          ∂                                              C                        ⁡                                                  (                                                                                    V                                                              d                                ⁢                                                                  xe2x80x83                                                                ⁢                                c                                                                                      ,                            z                                                    )                                                                                                            ∂                      z                                                        ⁢                                      V                                          a                      ⁢                                              xe2x80x83                                            ⁢                      c                                        2                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      xe2x80x83                                    ⁢                  ω                  ⁢                                      xe2x80x83                                    ⁢                  t                                +                                                                                                      ⁢                                                1                  2                                ⁢                                                                            ∂                      2                                        ⁢                                          C                      ⁡                                              (                                                                              V                                                          d                              ⁢                                                              xe2x80x83                                                            ⁢                              c                                                                                ,                          z                                                )                                                                                                                        ∂                      V                                        ⁢                                          ∂                      z                                                                      ⁢                                                      V                                          a                      ⁢                                              xe2x80x83                                            ⁢                      c                                        3                                    ⁡                                      (                                                                  cos                        ⁢                                                  xe2x80x83                                                ⁢                        3                        ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            +                                              cos                        ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                              )                                                              ]                                                          (        7        )            
Accordingly, there exists the third harmonic (3xcfx89) component given by                     F        =                              -                          1              8                                ⁢                      (                                                                                ∂                    2                                    ⁢                                      C                    ⁡                                          (                                                                        V                                                      d                            ⁢                                                          xe2x80x83                                                        ⁢                            c                                                                          ,                        z                                            )                                                                                                            ∂                    V                                    ⁢                                      ∂                    z                                                              ⁢                              V                                  a                  ⁢                                      xe2x80x83                                    ⁢                  c                                3                            ⁢              cos              ⁢                              xe2x80x83                            ⁢              3              ⁢                              xe2x80x83                            ⁢              ω              ⁢                              xe2x80x83                            ⁢              t                        )                                              (        8        )            
Therefore, information corresponding to an image of differential capacitance (∂C/∂V) can be obtained by detecting the third harmonic (3xcfx89) component.
The measuring apparatus according to the present invention is designed to measure values of a physical property of a sample by placing a probe and the sample close to or in contact with each other and characterized in that the apparatus includes at least one oscillator for applying an AC voltage of angular frequency xcfx89 between the probe and sample, force detection means for detecting a force produced by interaction between the probe and sample, and harmonic component extraction means for extracting a harmonic component nxc3x97xcfx89 (nxe2x89xa73) contained in the output from the force detection means.
Other objects and features of the invention will appear in the course of the description thereof, which follows.